The physics behind an electric motor and induced emf?

I am having trouble understanding a process in the electric motor. using this website as a frame of reference (http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html), as an electric current is passed into that magnetic field, shouldn't the current also be creating a magnetic field, and does that magnetic field interfere with the magnetic field already present?

Also when the coil in the magnetic field begins spinning is that what is causing the change in magnetic flux? If so, as that flux is changing should a back emf be induced, and if so again through what medium does that back emf travel? Sorry for so many questions I appreciate any help.

The field produced by the current plays no part in the interaction of a current in an externally applied magnetic field. Note the equation relating the force on a current to the external field.

The change in the magnetic flux is changing due to the motion of the coils in the rotor and/or the changing current and this does produce a back emf. This back emf is across the windings of the motor. This emf is a real issue for motor with a large inductance . When you turn off the motor the back emf can be so large as to cause an arc across the switch or even the windings.

The field produced by the current plays no part in the interaction of a current in an externally applied magnetic field. Note the equation relating the force on a current to the external field.

The change in the magnetic flux is changing due to the motion of the coils in the rotor and/or the changing current and this does produce a back emf. This back emf is across the windings of the motor. This emf is a real issue for motor with a large inductance . When you turn off the motor the back emf can be so large as to cause an arc across the switch or even the windings.

Does the back emf travel in the opposite direction as the original current, literally reducing it, or do they travel in different paths?

First of all, to eliminate any thinking about counter effects of currents, I ask that you stop thinking of the north and south poles shown in the figure as coming from an electromanget excited by some current and instead think of them as being permanent magnet and that's it...no wires, no current...i.e., a permanent magnet motor.

O.k., then...now, keep the following two things in mind:

A motor is a device that converts electric (current) energy into mechanical (rotational) energy.
A generator is a device that converts mechanical (rotational) energy into electric energy.

If we want to talk about a motor, we need a source of emf to inject a current. We inject this current into the wire loop which produces a magnetic field of its own...the direction of this magnetic field is such that when interacting with the existing one together they produce a torque on the wire making it spin. And, yes, once the loop is rotating, it will experience a changing flux which will induce an emf which will oppose the source emf being used to push the current in the first place.

If we want to talk about a generator, then, using the exact same figure and device, we "inject" mechanical (rotational) energy to the shaft of the wire loop, once rotating, it will experience a change in magnetic flux that will produce an emf and you will be able to get a current out of the wire loop if you connect a load to it. If you apply the right-hand-rule, you should notice that the current induced in the wire loop produces a magnetic field that when interacting with the existing one produces a torque that opposes the external torque being injected into the shaft.